So here's a question I had. Let's say I have a quantum mechanical system which obeys the Schrodinger equation.
$$ \hat H \psi = \hat T \psi + \hat V \psi $$
where $\hat H$ is the Hamiltonian, $\hat T \psi $ is the kinetic energy and $\hat V \psi $ is the potential. Let's say I wish to use this system as a quantum computer to perform some calculation. Now, let's I put the quantum computer itself into superposition? Now one may (reasonably) argue against this: How does one put the Hamiltonian this into superposition?
Quantum Field Theory! If I second quantize the Hamiltonian then I can have of quantum mechanical theory with superimposed particle numbers.
Now that I've superimposed the quantum computer. Is there a relation between the computation done by the original quantum computer and the super imposed quantum computer? Can someone refer me a paper where such an exploration has been done?